If the sum of $n$ terms of an AP is $2 n$ $^{2}$ $+ 5 n$ , then its $n$ th term is

4 n - 3

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3 n - 4

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4 n + 3

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3 n + 4

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Solution

The correct option is C $4 n + 3$
Given $S_{n} = 2 n^{2} + 5 n$

$S_{n - 1} = 2 {(n - 1)}^{2} + 5 (n - 1)$

$= 2 (n^{2} - 2 n + 1) + 5 n - 5$

$= 2 n^{2} - 4 n + 2 + 5 n - 5$

$= 2 n^{2} + n - 3$

Now, $t_{n} = S_{n} - S_{n - 1}$

$= 2 n^{2} + 5 n - (2 n^{2} + n - 3)$

$= 2 n^{2} + 5 n - 2 n^{2} - n + 3$

$= 4 n + 3$

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